Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}x+5y &= -9 \\ 2x-9y &= 1\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $2x = 9y+1$ Divide both sides by $2$ to isolate $x$ $x = {\dfrac{9}{2}y + \dfrac{1}{2}}$ Substitute this expression for $x$ in the first equation. $({\dfrac{9}{2}y + \dfrac{1}{2}}) + 5y = -9$ $\dfrac{9}{2}y + \dfrac{1}{2} + 5y = -9$ Simplify by combining terms, then solve for $y$ $\dfrac{19}{2}y + \dfrac{1}{2} = -9$ $\dfrac{19}{2}y = -\dfrac{19}{2}$ $y = -1$ Substitute $-1$ for $y$ in the top equation. $x+5( -1) = -9$ $x-5 = -9$ $x = -4$ The solution is $\enspace x = -4, \enspace y = -1$.